arXiv subjects

Bartłomiej A. Siudeja

Publications and source records attributed to Bartłomiej A. Siudeja.

2 recordsLinked to original sources

arXiv2016

Pólya's conjecture fails for the fractional Laplacian

The analogue of Pólya's conjecture is shown to fail for the fractional Laplacian (-Delta)^{alpha/2} on an interval in 1-dimension, whenever 0 < alpha < 2. The failure is total: every eigenvalue lies below the corresponding term of the Weyl asymptotic. In 2-dimensions, the fractional Pólya conjecture fails already for the first eigenvalue, when 0 < alpha < 0.984.

math.SP↗

arXiv2015

Trace estimates for unimodal Lévy processes

We give two-term small-time approximation for the trace of the Dirichlet heat kernel of bounded smooth domain for unimodal Lévy processes satisfying the weak scaling conditions.

math.FA↗